Unit 4 Flashcards
traveling wave
A wave that propagates through space
standing wave
A wave that vibrates in a fixed region, has boundary conditions
fundamental
n=1, standing waves with the fewest nodes
de Broglie wavelength for matter waves
λ=h/mv (mv=momentum, kg/s)
node
-A region of no vibration (of zero amplitude) of a standing wave
-the higher the n, the more numerous the nodes, the shorter the wavelength, the higher the frequency, the higher the energy
Heisenberg uncertainty principle
∆x∆p > h/4π
∆x
uncertainty in x, position
∆p
uncertainty in p, momentum (mv)
uncertainty ∆
full width half max of probability curve
observe particle nature
measure position, small ∆x, large ∆p
observe wave nature
diffraction or interference, small ∆p, large ∆x
indeterminate
If an observable property does not have a definite value under certain experimental conditions, it is said to be indeterminate
wave packet
-a group of superposed waves which together form a traveling localized disturbance, especially one described by Schrödinger’s equation and regarded as representing a particle
-can broaden with time or collapse upon measurement
how something appears depending on what experiment we do
cannot observe both wave and particle nature at same time
Amplitude (Ψ)
Ψ(x)= Amax(sin(2πx/λ))
Probability
Ψ^2
Uncertainty principle
-position (x) and momentum (p) cannot be determined exactly at same time
-there is a limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known
Quantum weirdness
-a qm particle (ex. an electron) is described by a wave function (amplitude vs position), Ψ(x)
-qm particle can exist as a superposition of “possibility” states described by a wave
-Amplitude= wave1 + wave2 + wave3…
Before a measurement
Ψ(x)= Ψ1(x) + Ψ2(x) + Ψ3(x) (superposition)
After a measurement
Ψ(x)= Ψi(x), where i=1, 2, 3, … (no superposition)
Complementary principle
-some experiments always detect the wave nature of wave particles, while others always detect the particle nature
-no experiment can detect both
